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Is it possible,starting from any of the 64 squares of the chessboard, to move a knight such that it occupies every square exactly once and return to the initial position? If so, give one such tour.

I don't have any idea

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HINT
Yes, it is possible. I would encourage you to draw a chess board and start. Here's a hint: the corner moves are all prescribed.

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  • $\begingroup$ Is there a smarter solution than just an exhibition? Exhibition is hard. As a graph theory question you can interpret the board as a graph with spaces as vertices which are adjacent if the knight can move from one to the other. Then the question asks for a Hamiltonian cycle. You know the graph is bipartite with 32 vertices on each side, but no obvious properties seem to imply the existence without writing out a tour. Is there a non-constructive proof?? $\endgroup$ – spitespike Jul 17 '14 at 20:12

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